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Hints?

Hello Guest!

I tried a bit to answer the problem, but couldn't exactly figure it out. 

I found a previous post that is extremely similar. 

https://web2.0calc.com/questions/help-asap_64

I'm sorry I couldn't help. 

=^._.^=

Hello Guest!

Let's start by making the question a bit simpler. 

There are 12 people who shake hands once with each other. How many handshakes are there? 

Another way of looking at this problem is how many ways can we choose 2 people?

There are 12 ways to choose the first person and 11 ways to choose the second person. 

12*11 = 132

However, we must remember that choosing person a first and then person b is the same as choosing person b first, then person a. 

So, we divide by 2. 

132/2 = 66

Our final answer is 66 handshakes. 

I hope this helped. :)))

=^._.^=

I'm new to this forum too (just joined a couple days ago). 

I'd love to make some friends too, everyone seems so nice. 

During winter break, this forum helped me with math so much, so I decided to join and see if I could help others too. 

Thank you to everyone who is a part of this wonderful community. 

I hope everyone has a fantastic 2021. :)))))

=^._.^=

Hello Guest!

To start, let's turn the equation to the form ax^2 + bx + c = 0 so we can apply the quadratic equation. 

x(x - 3) = 2

x^2 - 3x = 2

x^2 - 3x - 2 = 0. 

Now we just plug everything in. :))))

Here's the formula if you need it: https://en.wikipedia.org/wiki/Quadratic_equation#/media/File:Quadratic_formula.svg

x = (3 + sqrt(17))/2 or x = (3 - sqrt(17))/2

Now, we just do addition. 3 + 17 + 2 = 22.

I hope this helped. :)))

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(1, 4, 9, 16, 36, 81, 144, 324, 729, 1296, 2916, 6561, 11664, 26244, 59049, 104976, 236196, 944784)=18 such perfect squares.

Sorry there is a typo, for r3, it is $r$

Hello Guest!

Since a square has 4 congruent side lengths. Thus, each side length is 150/4 = 37.5. 

As we see from the image, the longer side length of the rectangle is the same length of the square side length. (37.5) 

4 of the smaller sides of the rectangle is equal to the length of the square side length (37.5/4 = 9.375) 

In each perimeter rectangle, there are 2 long lengths and 2 short lengths. 

9.375*2 + 37.5*2 = 93.75. 

I hope this helped. :))))

=^._.^=

Well, find the side length of the square, 150/4=37.5, the four congruent rectangles divide the 37.5 to 37.5/4=
9.375, 9.375+37.5+9.375+37.5= 93.75

18  -  6.5  -  1.15n   ≥   5.75

11.5  -  1.15n   ≥   5.75

                                            Subtract  11.5  from both sides of the inequality.

-1.15n  ≥  -5.75

                                            Divide both sides by  -1.15  and flip the inequality sign.

n   ≤  5

The number candy bar packages must be less than or equal to  5  The maximum number should be 5.

At least thats what I think

Thank you :p

Yes it was funny the first time I heard it, but now I hear it every day lol

3x4y3 – 48y3 It would be = 3y3(x4 – 16). right?

Maybe you mean   3x^4y^3 – 48y^3 It would be = 3y^3(x^4 – 16). right?

which is

\(3x^4y^3 – 48y^3 = 3y^3(x^4 – 16) ??\)

Yes that is correct.

I have not heard this before. I think it is funny  

Maybe not twice a day funny.....   

Angle PQR = 128 ⁴/₇ degrees. ( If the letters P, Q, R are in alphabetical order.)

The smallest possible value of angle PQR = 25.71428571 degrees

angle B = 168 degrees

The equation of the circle is (x - r)^2 + y^2 = r^2

==> 2(x - r) + 2y*y' = 0

The equation of the ellipse is x^2 + 5y^2 = 6

==> 2x + 10y*y' = 0

Matching the derivatives, we get r = 4/5.

The area of triangle AG₂G₃ = 3.33333333334 square units

Using variational calculus, the answer works out to 18.

Angle AHB = 106º  

50 that the answer

2^1001 - 1= 23 × 89 × 127 × 911 × 6007 × 8191 × 724153 × 112 901153 × 23140 471537 × 158822 951431 × 581283 643249 112959 × 5 782172 113400 990737 × 1820 949348 989208 563134 934454 867370 417241 731442 757253 769027 660122 025220 531154 643424 727557 175913 816984 478330 956518 484750 019883 125787 765755 778716 216864 601050 903144 122991 701474 321184 972747 689246 938140 437077 841940 203833 (214 digits) (Composite)

2^7 - 1 = 127

Therefore the GCD of [2^1001 - 1,  2^7 - 1]==127

Rationalize the denominator of 5/(3 - sqrt(3)), and write your answer in the form (A + B*sqrt(3))/C where the fraction is in lowest terms. What is A + B + C?     

Multiply both the numerator and

the denominator by (3 + sqrt(3)) 

This gets the radical out of the

denominator. 

         5                (3 + sqrt(3))  

——————  •  ——————  

(3 – sqrt(3))        (3 + sqrt(3))  

5 • (3 + sqrt(3))         15 + (5 • sqrt(3)  

———————   =   ———————  

      9 – 3                             6  

So the answer to "What is (A + B + C)?" is (15 + 5 + 6) which totals 26.  

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